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Vroman, Annelies; Deschrijver, Glad; Kerre, Etienne E.

A solution for systems of linear fuzzy equations in spite of the non-existence of a field of fuzzy numbers. (English) Zbl 1077.03033

Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 13, No. 3, 321-335 (2005).
It is well known that the fuzzy numbers, if combined with the usual fuzzy arithmetic, do not form a field due to the fact that the concept of inverse of a fuzzy number does not exist. Despite the lack of inverses, the authors propose a method to find an approximate solution of a system of linear fuzzy equations, making also a comparison with a method of J. J. Buckley and Y. Qu [Fuzzy Sets Syst. 43, No. 1, 33–43 (1991; Zbl 0741.65023)].
Reviewer: Salvatore Sessa (Napoli)

Cited in 4 Documents

MSC:

03E72 Theory of fuzzy sets, etc.
15A06 Linear equations (linear algebraic aspects)
65F05 Direct numerical methods for linear systems and matrix inversion

Keywords:

fuzzy number; linear fuzzy equation; fuzzy arithmetic; approximate solution

Citations:

Zbl 0741.65023
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\textit{A. Vroman} et al., Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 13, No. 3, 321--335 (2005; Zbl 1077.03033)
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References:

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